TEST SERIES round-1

TOPIC :CIRCULAR MOTION & + GRAVITATION

TEST ID –UT CLASS - XII

TEST NO -48 Pattern:BOARD Dr.Moin Sir

Q1] Give the response to the following MCQ’s [07 M]

1. When a body performs a U.C.M

(A) its velocity remains constant

(B) Work done oh it is zero

(D) no force acts on it

2. The gravitational force between two bodies is _______

(A) attractive at large distance only

(B) attractive at small distance only

(D) attractive at all distances large or small

3. Which of the following statements about the centripetal and centrifugal forces is correct?

(A) Centripetal force balances centrifugal force.

(B) Both centripetal force and centrifugal force act

in the same frame of reference.

centrifugal force.

(D) Centripetal force is experienced by the

observer at the centre of the circular path

described by the body.

4. A geostationary satellite

(A) revolves about the polar axis.

(B) has a time period less than that of the near earth satellite.

(D) is stationary in the space.

5. If a cycle wheel of radius 0.4 m completes one revolution in 2 seconds, then acceleration of the cycle is

(A) 0.4 p m/s (B) 0.4 p2 m/s2

6. Acceleration due to gravity above the earth’s

surface at a height equal to the radius of the earth is.

(A) 2.5 m/s2 (B) 5 m/s2

7. Angular speed of the second hand of a watch is

(A) p/60 rad/s (B) p/30 rad/ s

Q2] Attempt Any six of the following [12M]

1. State Kepler’s law of orbit and law of equal areas.

2. Derive the expression for max safe velocity on horizontal curve road.

3. Discuss the projection of satellite.

4. State and explain newtons law.

5. Derive the expression for acceleration due to gravity.

6. Calculate the acceleration due to gravity at the surface of the earth from the given data.

[Mass of the earth = 6 x 1024 kg,

Radius of the earth = 6.4 × 106 m,

G = 6.67 × 10–11 Nm2/kg2]

7. Calculate the angular velocity and linear velocity of a tip of minute hand of length

10 cm.

Q3] Attempt Any Three of the following [09M]

1. Derive the expression for max safe velocity for banked curve road.

2. Derive the expression for escape velocity for a satellite moving at height h around the earth.

3. Calculate the maximum speed with which a car can be safely driven along a curved road of radius 30 m and banked at 30° With the horizontal [g = 9.8 m/s2]

4. You are given the following data:

g = 9.81 ms–2, Re = 6.37 × 106 m, the distance to the moon R = 3.84 × 108 m and the time period of the moon’s revolution is 27.3 days. Obtain the mass of the earth ME in two different ways.

[G = 6.67 × 10–11 Nm2/kg2]

Q4] Attempt Any One of the following [07M]

1.Derive the variation of acceleration due to gravity with height, depth,latitude.

2. Define binding energy .Obtain an expression for the binding energy of a satellite orbiting the earth at a certain height.